"Sophus Lie" is an article from Science, Volume 9 . View more articles from Science . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-1625847

Source: http://www.jstor.org/stable/10.2307/1625847

"Biography: Sophus Lie" is an article from The American Mathematical Monthly, Volume 6 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2967890

Source: http://www.jstor.org/stable/10.2307/2967890

9
9.0

Sep 5, 2013
09/13

by
Engel F., Heegaard P. (eds.)

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"Some Reminiscences in Regard to Sophus Lie" is an article from The American Mathematical Monthly, Volume 6 . View more articles from The American Mathematical Monthly . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2968038

Source: http://www.jstor.org/stable/10.2307/2968038

116
116

Sep 19, 2013
09/13

by
Joel Merker

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A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.

Source: http://arxiv.org/abs/0910.0801v2

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108

Sep 21, 2013
09/13

by
C. Wafo Soh

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We obtain iso-spectral Euler-Bernoulli beams by using factorization and Lie symmetry techniques. The canonical Euler-Bernoulli beam operator is factorized as the product of a second-order linear differential operator and its adjoint. The factors are then reversed to obtain iso-spectral beams. The factorization is possible provided the coefficients of the factors satisfy a system of non-linear ordinary differential equations . The uncoupling of this system yields a single non-linear third-order...

Source: http://arxiv.org/abs/0709.1155v1

8
8.0

May 20, 2019
05/19

by
Stubhaug, Arild, 1948-

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xi, 555 pages : 25 cm

Topics: Lie, Sophus, 1842-1899, Lie, Sophus, Lie, Sophus 1842-1899, Mathematicians, Mathematicians --...

49
49

Sep 18, 2013
09/13

by
Robert L. Bryant; Gianni Manno; Vladimir S. Matveev

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We give a complete list of normal forms for the 2-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie.

Source: http://arxiv.org/abs/0705.3592v2

No more published

Topic: Contact transformations

40
40

Sep 18, 2013
09/13

by
Boris M. Doubrov; Boris P. Komrakov

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The paper is devoted to the complete classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool we use the abstract theory of filtered and graded Lie algebras. We also describe all differential and integral invariants of new Lie algebras found in the paper and discuss the...

Source: http://arxiv.org/abs/math/9903198v1

46
46

Jul 20, 2013
07/13

by
Jan Draisma

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This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are a recurring theme in 20th-century research on Lie algebras. I will focus on so-called transitive or even primitive Lie algebras, and explain their theory due to Lie, Morozov, Dynkin, Guillemin, Sternberg, Blattner, and others. This paper gives...

Source: http://arxiv.org/abs/1107.2836v2

0
0.0

Jun 30, 2018
06/18

by
José F. Cariñena; Fernando Falceto; Janusz Grabowski; Manuel F. Rañada

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After a short review of the classical Lie theorem, a finite dimensional Lie algebra of vector fields is considered and the most general conditions under which the integral curves of one of the fields can be obtained by quadratures in a prescribed way will be discussed, determining also the number of quadratures needed to integrate the system. The theory will be illustrated with examples andbn an extension of the theorem where the Lie algebras are replaced by some distributions will also be...

Topics: Classical Analysis and ODEs, Mathematical Physics, Nonlinear Sciences, Exactly Solvable and...

Source: http://arxiv.org/abs/1701.03907

10
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The contribution of Emmy Noether, Felix Klein and Sophus Lie to the modern concept of symmetries in physical systems. by Hans A. Kastrup

Topics: symmetry, conservation law

138
138

Jul 20, 2013
07/13

by
Ercüment Ortaçgil

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We outline a framework which generalizes Felix Klein's Erlanger Programm which he announced in 1872 after exchanging ideas with Sophus Lie.

Source: http://arxiv.org/abs/math/0604223v3

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34

Sep 20, 2013
09/13

by
Vladimir S. Matveev

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We give a complete list of two-dimensional metrics that admit an essential projective vector field. This solves a problem explicitly posed by Sophus Lie in 1882.

Source: http://arxiv.org/abs/0802.2344v2

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47

Jul 20, 2013
07/13

by
Jan Hendrik Bruinier

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The present notes contain the material of the lectures given by the author at the summer school on ``Modular Forms and their Applications'' at the Sophus Lie Conference Center in the summer of 2004.

Source: http://arxiv.org/abs/math/0609763v1

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53

Jul 20, 2013
07/13

by
Hans Havlicek

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Starting with the classical circle geometry of Sophus Lie, we give a survey about some of the developments in the area of chain geometries during the last three decades.

Source: http://arxiv.org/abs/1304.1343v1

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33

Sep 21, 2013
09/13

by
Boris Kruglikov

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Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of Sophus Lie. Plenty of relations between them have been noticed and in this note a unifying approach will be discussed. It is rather close to the classical differential constraint method, but we provide certain rigorous results basing on recent advances in compatibility theory of non-linear overdetermined systems and homological methods for PDEs.

Source: http://arxiv.org/abs/0712.3425v1

4
4.0

Jun 28, 2018
06/18

by
Damien Broka; Ping Xu

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Symplectic realization is a longstanding problem which can be traced back to Sophus Lie. In this paper, we present an explicit solution to this problem for an arbitrary holomorphic Poisson manifold. More precisely, for any holomorphic Poisson manifold $(X, \pi)$, we prove that there exists a holomorphic symplectic structure in a neighborhood $Y$ of the zero section of $T^*X$ such that the projection map is a symplectic realization of the given Poisson manifold, and moreover the zero section is...

Topics: Differential Geometry, Mathematics, Complex Variables, Algebraic Geometry, Mathematical Physics,...

Source: http://arxiv.org/abs/1512.08847

40
40

May 16, 2018
05/18

by
Wussing, Hans

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In this book, Hans Wussing sets out to trace the process of abstraction that led finally to the axiomatic formulation of the abstract notion of group. His main thesis is that the roots of the abstract notion of group do not lie, as frequently assumed, only in the theory of algebraic equations; they are also to be found in the geometry and the theory of numbers of the end of the 18th and the first half of the 19th centuries. The book takes us from Lagrange via Cauchy, Abel, and Galois to Serret...

Topics: Group theory -- History, Groupes, Théorie des -- Histoire, Group theory, Groupes, Théorie des,...

California Digital Library

1,013
1.0K

Aug 22, 2008
08/08

by
Klein, Felix, 1849-1925; Ziwet, Alexander, 1853-1928

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I. Clebsch.--II-III. Sophus Lie.--IV. On the real shape of algebraic curves and surfaces.--V. Theory of functions and geometry.--VI. On the mathematical character of space-intuition, and the relation of pure mathematics to the applied sciences.--VII. The transcendency of the numbers [epsilon] and [pi].--VIII. Ideal numbers.--IX. The solution of higher algebraic equations.--X. On some recent advances in hyperelliptic and Abelian functions.--XI. The most recent researches in non-Euclidean...

Topic: Mathematics

35
35

Jul 26, 2018
07/18

by
Felix Klein; Alexander Ziwet

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Book from Project Gutenberg: The Evanston Colloquium: Lectures on Mathematics

Topics: Mathematics, QA, Mathematics

Source: https://www.gutenberg.org/ebooks/36154

10
10.0

Jun 30, 2018
06/18

by
Eldar Straume

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This is an expository treatise on the development of the classical geometries, starting from the origins of Euclidean geometry a few centuries BC up to around 1870. At this time classical differential geometry came to an end, and the Riemannian geometric approach started to be developed. Moreover, the discovery of non-Euclidean geometry, about 40 years earlier, had just been demonstrated to be a "true" geometry on the same footing as Euclidean geometry. These were radically new ideas,...

Topics: Mathematics, History and Overview

Source: http://arxiv.org/abs/1409.1140

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29

Sep 23, 2013
09/13

by
Joel Merker

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In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), to the Newtonian free particle equation Y_XX = 0. This result, preliminary to the deep group-theoretic classification of second order analytic ordinary differential equations, was parachieved later in 1896 by Arthur Tresse, a French student...

Source: http://arxiv.org/abs/math/0411165v3

3
3.0

Jun 28, 2018
06/18

by
Hubert Goenner

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A possible influence of Klein's Erlangen program on physical theories is investigated. While some connections are found, it is concluded that Lie's theory of transformation groups and Lie algebras have had a much larger impact. In this context, an extension to tangential Lie algebroids is discussed.

Topics: Physics, History and Philosophy of Physics

Source: http://arxiv.org/abs/1510.08319

Cornell University Library

620
620

Nov 7, 2009
11/09

by
Klein, Felix, 1849-1925; Ziwet, Alexander, 1853-1928; Klein, Felix, 1849-1925. Mathematik. English

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The metadata below describe the original scanning. Follow the "All Files: HTTP" link in the "View the book" box to the left to find XML files that contain more metadata about the original images and the derived formats (OCR results, PDF etc.). See also the What is the directory structure for the texts? FAQ for information about file content and naming conventions.

Topic: Mathematics

245
245

Jul 10, 2011
07/11

by
Lie, Sophus, 1842-1899

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Book from Project Gutenberg: Über Integralinvarianten und Differentialgleichungen Library of Congress Classification: QA

Topics: Differential equations, Integrals

Source: http://www.gutenberg.org/ebooks/25157

1,064
1.1K

Apr 13, 2008
04/08

by
Lie, Sophus, 1842-1899; Engel, Friedrich, 1861-1941

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Book digitized by Google and uploaded to the Internet Archive by user tpb.

Topics: Transformation groups, Continuous groups, Contact transformations

Source: http://books.google.com/books?id=pRkPAAAAIAAJ&oe=UTF-8

107
107

Nov 2, 2014
11/14

by
Lie, Sophus, 1842-1899

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Mode of access: Internet

Topics: bub_upload, Contact transformations

Source: http://books.google.com/books?id=Zm5tAAAAMAAJ&hl=&source=gbs_api

227
227

Feb 10, 2008
02/08

by
Sophus Lie

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Source: http://books.google.com/books?id=rhoLAAAAYAAJ&oe=UTF-8

229
229

May 28, 2008
05/08

by
Sophus Lie

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Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user tpb.

Source: http://books.google.com/books?id=UDIAAAAAQAAJ&oe=UTF-8

591
591

May 12, 2008
05/08

by
Lie, Sophus, 1842-1899; Engel, Friedrich, 1861-1941

texts

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eye 591

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Book digitized by Google and uploaded to the Internet Archive by user tpb.

Topics: Transformation groups, Continuous groups, Contact transformations

Source: http://books.google.com/books?id=eBgPAAAAIAAJ&oe=UTF-8

7
7.0

Oct 16, 2013
10/13

by
Lie Sophus, Scheffers G.

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194
194

May 4, 2008
05/08

by
Sophus Lie

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Source: http://books.google.com/books?id=LZALAAAAYAAJ&oe=UTF-8

15
15

Oct 16, 2013
10/13

by
Lie Sophus, Scheffers G.

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785
785

Mar 2, 2008
03/08

by
Lie, Sophus, 1842-1899; Engel, Friedrich, 1861-1941

texts

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Book digitized by Google and uploaded to the Internet Archive by user tpb.

Topics: Transformation groups, Continuous groups, Contact transformations

Source: http://books.google.com/books?id=GxkPAAAAIAAJ&oe=UTF-8

22
22

Mar 2, 2018
03/18

by
Lie, Sophus, 1842-1899

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Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen Vorwort, Inhaltsverzeichnis, Schlussvort

Topics: Differential equations, Infinitesimal transformations

14

Topic: Continuous groups

1,007
1.0K

Jan 26, 2008
01/08

by
Sophus Lie, Worm Müller, G. O. Sars

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: den, der, det, med, paa, som, die, ikke, sig, saa, paa den, dass die, die form, der form, theorie...

Source: http://books.google.com/books?id=dwoMAAAAYAAJ&oe=UTF-8

"Die Begriffe Gruppe und Invariante" is an article from American Journal of Mathematics, Volume 11 . View more articles from American Journal of Mathematics . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-2369418

Source: http://www.jstor.org/stable/10.2307/2369418

1,022
1.0K

Mar 19, 2008
03/08

by
Sophus Lie, Worm Müller, G. O. Sars

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: der, den, die, det, med, paa, som, eine, ikke, dass, der form, dass die, die form, paa den, theorie...

Source: http://books.google.com/books?id=kAcMAAAAYAAJ&oe=UTF-8

512
512

Mar 2, 2008
03/08

by
Lie, Sophus, 1842-1899; Scheffers, Georg, 1866-1945, ed

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eye 512

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Book digitized by Google from the library of the New York Public Library and uploaded to the Internet Archive by user tpb.

Topics: Differential equations, Transformations, Infinitesimal

Source: http://books.google.com/books?id=pgwAAAAAMAAJ&oe=UTF-8

14 32

Topics: Differential equations, Transformations, Infinitesimal

1,111
1.1K

May 25, 2008
05/08

by
Sophus Lie, Worm Müller, G. O. Sars

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: den, der, det, med, paa, som, die, sig, saa, ikke, den indre, den ydre, paa den, dass die, det...

Source: http://books.google.com/books?id=IwcMAAAAYAAJ&oe=UTF-8

208
208

Feb 3, 2008
02/08

by
Lie, Sophus, 1842-1899; Scheffers, Georg

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: Group theory, Groupes, Théorie des, Group theory

Source: http://books.google.com/books?id=yZgLAAAAYAAJ&oe=UTF-8

393
393

Jul 8, 2015
07/15

by
Niels Henrik Abel

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Book digitized by Google from the library of Oxford University and uploaded to the Internet Archive by user the-it.

Topics: Abel, Niels, Henrik, OEuvres Completes 1881 Sophus Lie

435
435

Aug 15, 2009
08/09

by
Lie, Sophus, 1842-1899; Scheffers, Georg, 1866-1945, ed

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topics: Differential equations, Transformations, Infinitesimal

Source: http://books.google.com/books?id=FDcNAAAAYAAJ&oe=UTF-8

575
575

Jul 24, 2009
07/09

by
Lie, Sophus, 1842-1899; Scheffers, Georg, 1866-1945

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Book digitized by Google from the library of Harvard University and uploaded to the Internet Archive by user tpb.

Topic: Contact transformations

Source: http://books.google.com/books?id=CpkLAAAAYAAJ&oe=UTF-8

14 21

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Topic: Continuous groups

1,201
1.2K

Mar 2, 2006
03/06

by
Lie, Sophus, 1842-1899; Engel, Friedrich, 1861-1941; Heegaard, Poul, 1871-1948; Engel, Friedrich 1861- Anmerkungen zum ersten Bande[-sechsten Band

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Vol. 1 , suppl.

Topic: Mathematics